9 problems

Consider a $W$-state droplet evolving under a general type II Hamiltonian, and let the droplet domain remain intact up to its melting time. Boundary-driven directional-motion conje…

For integers $p\geq1$, define … These operators are type II Hamiltonians when the relevant $\ket{W^{p'}}$ states are exact scars for $p\leq p'$. Independent-Hamiltonians conjecture…

Let an interacting type II Hamiltonian act on a $W$-state droplet, with its action localized at the droplet boundaries. Ballistic-motion and diffusive-melting conjecture. The inter…

The W-state signature conjecture. If such a translation-invariant Hamiltonian is tuned so that the zero-mode $|W_1\rangle$-like state and the product state…

Kitaev's no-go conjecture. No commuting strictly local Hamiltonian on a two-dimensional lattice with locally finite-dimensional degrees of freedom can realize a chiral topological…

Let $E_+$ be the set of positive exponents of the underlying Lie algebra, let $\varphi(z)$ be the twist function, and let $h^\vee$ be the dual Coxeter number. The quadratic Hamilto…

Let $n_c$ be the number of iterations required to obtain an accuracy satisfying $f_{n_c}(\lambda_0)>1-\epsilon$, where $D=\lambda_1-\lambda_0\ll 1$ is the difference between the tw…

Let $\gamma^\alpha$ be the matrices defining a representation of the Clifford algebra $C^{0,d}$, and let $M$ be a real antisymmetric mass term. Assume that…

Existence conjecture. For any $L_{0}$-regular spin chain there always exists a Hamiltonian which is $L_{0}$-local.